A Novel Model of Foam Flooding Considering Multi-Factors for Enhancing Oil Recovery

8/12/2019 A Novel Model of Foam Flooding Considering Multi-Factors for Enhancing Oil Recovery

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D o s s i e r

Second and Third Generation Biofuels: Towards Sustainability and CompetitivenessSeconde et troisime gnration de biocarburants : dveloppement durable et comptitivit

A Novel Model of Foam Flooding ConsideringMulti-Factors for Enhancing Oil Recovery

J. Wang1,2*, H. Liu1, H. Zhang1, G. Zhang3, P. Liu4 and K. Sepehrnoori2

1 MOE Key Laboratory of Petroleum Engineering in China University of Petroleum, Beijing 102249 - China2 Department of Petroleum & Geosystems Engineering, The University of Texas at Austin, Austin 78712 - USA

3 CNOOC Tianjin Branch Company, Tianjin 300452 - China4 Sinopec Shengli Oileld Branch Company, Shandong Dongying 257000 - China

e-mail: [email protected]

* Corresponding author

Abstract Foam flooding is a promising technique for achieving mobility control and diverting fluid

into low-permeability strata in post-water-flooding reservoirs. However, foam flow is very compli-

cated and is influenced by many factors which have not been studied and explored very rigorously

(i.e. permeability, surfactant concentration, foam quality, reservoir temperature, oil saturation,

water saturation and seepage velocity). Based on core flooding experiments of foam flowing and

blocking rules using two kinds of foaming agents, a novel model of foam flooding considering the

influences of the above factors is established and solved using a reservoir simulator which is formu-

lated using the IMPES method in conjunction with a Runge-Kutta method. Then, the validation is

performed by core flooding experiments in both the absence and presence of oil. Finally, the simula-

tor is used to investigate the effects of the permeability max-min ratio, ratio of vertical to horizontalpermeability, gas-liquid ratio, depositional sequence, foaming agent concentration, and reservoir

temperature.

Re sume Un nouveau mode` le dinjection de mousse conside rant de multiples facteurs afin

dame liorer la re cupe ration de pe trole Linjection de mousse est une technique prometteuse

pour atteindre un controle de la mobilite et de tourner le fluide dans des couches a` faible

perme abilite de re servoirs apre` s injection deau. Toutefois, le coulement de mousse est tre` s

complique et est influence par de nombreux facteurs qui nont pas e te e tudie s et explore s de

manie` re tre` s rigoureuse (a` savoir la perme abilite , la concentration en tensioactif, la qualite de

la mousse, la tempe rature du re servoir, la saturation en pe trole, la saturation en eau et la

vitesse de coulement). Sur la base dexpe riences dinjection de mousse dans des carottes et de

re` gles de blocage en utilisant deux types dagents moussants, un nouveau mode` le dinjection demousse qui tient compte des influences des facteurs ci-dessus est e tabli et re solu, en utilisant un

simulateur de re servoir base sur la me thode IMPES combine e a` la me thode Runge-Kutta.

Ensuite, la validation est re alise e par des expe riences dinjection dans des carottes a` la fois en

labsence et en pre sence de pe trole. Enfin, le simulateur est utilise pour e tudier les effets du

rapport max/min de perme abilite , du rapport de perme abilite verticale/horizontale, du rapport

gaz/liquide, des se quences de de pot, de la concentration de lagent moussant et de la

tempe rature du re servoir.

Oil & Gas Science and Technology Rev. IFP Energies nouvellesCopyright 2014,IFP Energies nouvellesDOI: 10.2516/ogst/2014025
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INTRODUCTION

Foam flooding is an EOR (Enhance Oil Recovery) tech-

nique taking foam as the displacing fluid. Foam not only

effectively decreases the mobility ratio of gas to oil but

also weakens the phenomena of gas channeling and

steam override [1, 2]. Moreover, due to the particular

mechanisms of foam generation and collapse, foam pre-sents the selective blocking features of big block and

small not block and water block and oil not block

when it flows in porous media [3], which is very favorable

for enhancing oil recovery. In the past few years, foam

flooding has been carried out in many pilots in China,

and most of them have shown a good performance [ 4].

In a study of foam triggering mechanisms, Kovscek

et al. [5] attributed triggering mechanisms of foam to

increasing the viscosity of the driving phase; Rossen

et al.[6] attributed the triggering mechanism to declining

gas phase mobility; Kovscek and Bertin [7] reported that

both increasing gas phase viscosity and decreasing thegas phase relative permeability take effect simulta-

neously, and hence they improved the models for foam

viscosity and the gas phase relative permeability. How-

ever, it is controversial that relative permeability and vis-

cosity are considered separately [8]. As can be seen from

these studies, it is recognized that the triggering mecha-

nism of a foam system is decreasing the gas mobility,

but many different approaches, e.g. modifying the gas

phase viscosity or gas phase relative permeability or

modifying both the gas phase viscosity and relative per-

meability are considered to achieve this mechanism.

Nevertheless, foam flow in porous media is a very com-plicated process, since the lamellae in the flowing state

will increase the viscosity of the driving phase and the

lamellae adsorbed on the pore surface will reduce gas rel-

ative permeability. Unfortunately, because of the sur-

rounding environment, especially the properties of the

rock and fluid, both mechanisms are difficult to distin-

guish and test by experiments. Therefore, the above

approaches for representing foam mechanisms are par-

tial and difficult to quantify. In this paper, the mobility

of the gas phase is considered as a whole to test and be

measured by the resistance factor. This method includes

increasing the viscosity of the displacing phase as well asdecreasing the gas relative permeability, avoids repeated

tests, and takes into account the effects of these two

mechanisms. Numerical simulation is a technique to

study the flow characteristics described by mathematical

models [9]. It has features of low cost, high efficiency and

good repeatability, and can demonstrate the entire com-

plex flow process. Because foam is a very complex system

where gas is the dispersed phase and liquid is the contin-

uous phase, accurate prediction is difficult. There are

several approaches to deal with its complexity. The first

approach is called population balance, which quanti-

fies the relation between foam mobility and foam texture

and all the mechanisms of creation and destruction of

liquid films, or lamellae [10-13]. It uses a differential

equation to represent foam texturein situ, but the basic

concept is consistent with the local-equilibrium version,

in which foam texture is an algebraic function of localconditions [6]. In all population balance models, the rate

of creation of lamellae depends on gas velocity through

pore throats where snap-off takes place [10-13]. The sec-

ond approach represents foam mobility as an empirical

function of many influence factors [14-17]. The third

approach is the fixed-Pc* model, which relies on the

relation between capillary pressure, foam texture and

foam mobility [18]. In essence, it is also a local-

equilibrium version of the population balance for strong

foams under conditions where capillary pressure domi-

nates foam texture and gas mobility [6]. The first

approach is more complex, and there is no way to sepa-rate the effects of lamella generation and destruction in

history-matching coreflood results [6]; the second

approach is simple, but it disregards the relation between

foam mobility and texture; the third approach is between

the other two, but it disregards the foam strength influ-

enced by many key factors. Based on the advantages

and disadvantages of the above three models, a synthe-

sized multi-factor foam model is presented. In the novel

model, the foam generation depends on the critical gas

velocity, which is a function of the aqueous phase mobil-

ity fraction [12]. The foam collapse depends on limiting

capillary pressure, at which foam collapses abruptly[19]. SinceSwis related toPcthrough the capillary-pres-

sure functionPc(Sw), this means that foam remains at a

given water saturation Sw* Sw(Pc*). Foam strength,which is influenced by permeability, surfactant concen-

tration, foam quality, reservoir temperature and oil sat-

uration, affects the foam mobility, which is evaluated by

the foam resistance factor. Therefore, a foam resistance

factor model derived from our coreflood experiments

using two kinds of foam agents is used to represent foam

strength features [20]. The advantages of this approach

reflect the competing goals of simplicity and complete-

ness; however, the model is not able to describe slow gen-eration or destruction processes thoroughly, considering

the influence of flow velocity on foam mobility.

Finally, the model validation was performed by core

flooding experiments; the factors which affect the EOR

effects of foam flooding were investigated using the

novel model: the permeability max-min ratio, the ratio

of vertical to horizontal permeability, gas-water ratio,

foaming agent concentration, temperature and deposi-

tional sequence.

2 Oil & Gas Science and Technology Rev. IFP Energies nouvelles


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1 GOVERNING EQUATION

1.1 Mass Conservation Equations

The assumptions imposed on the flow equations include:

four components: oil, water, gas and surfactant;

gas, water and surfactant generate foam which

reduces the gas mobility; the whole process is isothermal, and the energy trans-

fer is neglected;

fluid flow obeys the generalized Darcys law;

phase equilibrium is reached instantaneously;

foam only affects mobility (the ratio of gas relative

permeability to viscosity).

Mass balance equation for the oil phase:

r ~kkroloBo

rUo

! qo

@

@t

/So

Bo

1

Mass balance equation for the aqueous phase:

r ~kkrwlwBw

rUw

! qw

@

@t

/Sw

Bw

2

Mass balance equation for the gas phase:

r ~kkrg

lgBgRgrUg

! qg

@

@t

/Sg

Bg

3

Mass balance equation for the surfactant (foaming

agent):

r cs~vw r ~ds/Swrcs

qwcs@ /Swcs

@t

@qr 1 / cs

@t

4

In whichk is the absolute permeability, lm2;krlis the

relative permeability of phasel;llis the effective viscosity

of phase l, mPas; Bl is the formation volume factor ofphase l, m3/m3; 5 is the divergence operator; ql is the

sourceand sink forphase l, m3/(daym3); Rg is the gas resis-tance factor;Ul is the potential of phasel,MPa; Sl isthesat-

uration of phase l; u is porosity; cs is the surfactant

concentration, kg/m3; ds is the diffusion coefficient of

the surfactant, m2/s; qr is the rock density, kg/m3;

csis the adsorption concentration of the surfactant, kg/kg.

1.2 Auxiliary Equations

Let Sw, So and Sg be water, oil and gas saturation,

respectively. Then the saturation constraint equation is:

So Sw Sg 1 5

Also,pw,po and pgare water, oil and gas phase pres-

sures, respectively; the capillary pressure equations are:

pcow po pw 6

pcgo pg po 7

In whichpcowis the capillary pressure between oil andwater, Pa; andpcgo is the capillary pressure between gas

and oil, Pa.

1.3 Process Mechanism Models of Foam Flooding

1.3.1 Foam Resistance Factor

The effects of different factors on foam block character-

istics are obtained by experiments using two kinds of sur-

factants. One is sodium dodecyl sulfate (#1) and another

is an industrial foaming agent used in the Henan oilfield

(#2). Then, a range of variograms and their correctionmodels are applied to fit the relationship linking the

foam resistance factor and other factors. The undeter-

mined coefficients can be obtained using DATAFIT

software [21] based on experimental results. Because of

the consistency in physical meaning among variograms,

the foam generation and collapse mechanisms, this

method evades the defect from the conventional mathe-

matical regression method that can merely be applied to

a local scale but not to the extended area.

Resistance Factor vsFoaming Agent Concentration

A logistic model is a straightforward model used to fore-

cast the population growth and presents an S tendency

which can be divided into elementary, acceleration

transfer, deceleration and saturation periods. The adsor-

bance of active molecules on the gas/liquid interface has

a similar trend, which determines the variation of foam

blocking ability. As a result, the blocking capacity

increases as the surfactant concentration increases

although there is a break in the curve at about 0.5%

by weight. Based on experimental results (Fig. 1) and

the Critical Micelle Concentration (CMC) introducedas a characteristic parameter, a logistic function was

used to model the relationship between the resistance

factor and foaming agent concentration:

Rfcs Rf

csCMC

1 a expr cs 8

Using DATAFIT and the above model, the undeter-

mined coefficients were obtained. For surfactant #1

J. Wanget al. / A Novel Model of Foam Flooding ConsideringMulti-Factors for Enhancing Oil Recovery

3


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a1=100 and r1=19.5; and for surfactant #2, a2=230

andr2=16.

Resistance Factor vsFoam Quality

Khatibet al. [19] showed that at a given gas flow rate, the

foam resistance factor increases slightly with increasing

foam quality ranging from 50% to 98%. De Vries and

Wit [22] reported that at an imposed total flow rate,

the foam resistance factor increases as foam qualityincreases until the break point; beyond that it decreases.

Chang and Grigg [23] found that the foam resistance fac-

tor increases with increasing foam quality ranging from

33.3% to 80%. We found that the resistance factor first

increases and then decreases as the foam quality

increases, and the break point is at about 80%. However,

it is challenging for the foam quality to reach above 80%

in foam flooding pilots. Hence, the proportional region

between the resistance factor and foam quality is of con-

cern from the practical application viewpoint. Derived

from the data of this region (Fig. 2), the variation resem-

bles the exponential variogram model. After deliberatingthe endpoint feature, the relationship between the resis-

tance factor and foam quality is:

Rfg 1 Rfjggc 1 exp 3g

b

9


mined coefficients were obtained. For surfactant #1,

b1 = 60; and for surfactant #2, b2 = 45.

Resistance Factor vsPermeability

One merit of the foam used for EOR is big block and

not small block, meaning foam has a better blocking

ability in high-permeability regions or layers and the

blocking ability nearly disappears in low-permeability

regions or layers. This indicates shear thinning of the

foam, which has been experimentally confirmed by many

researchers [24-28]. In order to characterize the relation

between the resistance factor and permeability (Fig. 3),

dimensionless permeability (kD) is used. The relation

between the resistance factor and dimensionless perme-

ability is:

Rfk Rjkkc 1 1 kD

1 mkDn

10

kD k=kc 11



m1=3 and n1=2; and for surfactant #2, m2=8.5 andn2=1.05.

Resistance Factor vsTemperature

Influencing mechanisms of temperature on foam resis-

tance are diverse [29]. First of all, the dissolving capacity

increases as the temperature increases, so the adsorbance

of active molecules on the gas/liquid interface decreases,

350

300

250

200

150

100

50

00 0.2 0.4 0.6 0.8 1.0

Surfactant concentration (wt%)

Experimental value of surfactant #1


Calculation value of surfactant #1


Res

istancefactor

Figure 1

Comparison between experiments and the model of the

resistance factor for different surfactant concentrations.

300

250

200

150

100

50

00 20 40 60 80 100

Foam quality (%)





Resistancefactor

Figure 2

Comparison of experiments and the model of the resistance

factor for different foam qualities.



5/17

which results in a decrease in the strength of the lamellae.

In addition, an increase in temperature will accelerate

the drainage rate of liquid from lamellae to the liquid

phase and promotes the collapse and coalescence of

the bubbles. Moreover, an increase in temperature will

also speed up the degradation of the foaming agent.

Friedmann et al. [12] and Maini and Ma [30] reported

that the foam resistance ability largely decreases as the

temperature increases in porous media. Based on exper-

imental results and the break point denoted as Tr

(Fig. 4), the relation between temperature and foamquality is modeled as:

RfT Rf

TTr

1 exp Tab

12



a1=140 and b1=30; for surfactant #2, a2=70 and

b2=38.

Resistance Factor vsOil Saturation

The mechanisms by which oil affects the foam stability

are diverse. Some studies have confirmed that the foam

can be generated in the presence of oil by selecting

appropriate foaming agents [31-34]. Some studies have

stated that foam can be generated when the oil satura-

tion is below a critical value [35-37], but some other stud-

ies have shown that foam is generated at relatively high

oil saturation [34,38,39]. The characteristics of foaming

agents and oil samples used in the experiments may

cause these differences. In general, it is commonly agreed

that the presence of oil is detrimental to the foam stabil-

ity [35,36,38,40], and our experimental results also sup-port this view. Therefore, oil saturation is more likely to

be regarded as an influencing factor of the resistance fac-

tor than a critical condition of foam collapse. Based on

experimental results (Fig. 5), the foam resistance factor

exponentially decreases as the oil saturation increases,

and different values of c will be achieved for different

foaming agents and oil samples:

RfSo RfjSo0 expc So 13

300

250

200

150

100

50

00 50 100 150 200 250 300 350

Temperature (oC)





Resistancefactor

Figure 4


factor for different temperatures.

300

250

200

150

100

50

00 0.1 0.2 0.3 0.4 0.5 0.6

Oil saturation





Resistancefactor

Figure 5


factor for different oil saturation ratios.

500

400

300

200

100

00 5 10 15

Permeability (m2)





Res

istancefactor

Figure 3


factor for different permeabilities.


5


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c1=9.0; for surfactant #2, c2=9.2.

Seepage Velocity - The Critical Generation Conditionof Foam

The generation mechanisms of foam in porous mediainclude lamellae snap-off, lamellae lag and lamellae

trapping. Many experiments indicated that the lamel-

lae snap-off or lamellae flow will not occur until the

pressure or velocity overpasses the critical value. In

fact, it is a triggering mechanism. Once foam is in

place, velocity can be reduced, but the foam remains.

Fridmann et al. [12] found that the critical velocity

increases as the liquid volume fraction decreases

according to the following:

vgc 1:52

V1:54L

14

where vgc is the critical velocity of foam generation,

m/day, andVL is themobility fraction of theaqueousphase.

Water Saturation - The Critical Collapse Conditionof Foam

Based on the DLVO theory [41,42], the collapse of foam

is related to critical capillary force. When the practical

capillary force exceeds the critical value, foam will col-

lapse. However, the capillary force is a function of water

saturation; the higher the water saturation, the smallerthe capillary force will be. Therefore, once the water sat-

uration is lower than the critical value corresponding to

the critical capillary force, the foam will collapse. Khatib

et al.[19] found that the critical capillary force logarith-

mically decreases as the permeability and gas velocity

increase, which also reflects the shear-thinning charac-

teristics of the foam system. Based on the definition of

the Leverett J-function and the empirical relation of

the Leverett J-function [43, 44], we have:

J S

w

Pc

rgwcos hffiffiffiffik

/s

aJSw Swc

1 Swc bJ

15

Khatibet al.[19] also found that the critical capillary

pressure logarithmically decreases with increasing per-

meability (may reflect the effect of the pore structure)

and gas velocity, which also reflects the shear-thinning

characteristic of foam:

Pc k; vg

a1lnkvg b1 16

Substituting Equation (16) into Equation (15), the

limiting water saturation was obtained to be:

Sw 1 Swc a1lnkvg b1

aJrgwcos h

ffiffiffiffik

/

s" # 1bJ

Swc 17

In Equations (15-17), J(Sw*) is the J function; Pc* is

the critical capillary force, MPa; vg is the gas velocity,cm/s; rgw is the gas-water interfacial tension, mN/m; h

is the wetting angle; a1, b1, aJ and bJ are undetermined

coefficients;Sw* is the critical water saturation.

Multi-factor Gas Mobility Model

Based on a previous study [6], the resistance factor of the

gas phase in porous media with the presence of

foam is:

Rg

1 Sw Sw e and v< vgc

1 Rkf1SwS

we

2eSw e >>>>:

18

wheree is a special parameter; e = 0.001 was used in this

paper. It will not affect the simulation of the displacement

effect. It is only used to avoid the jumpof the calculatedgas

mobility due to the actual water saturation fluctuation

above and below the critical value. The influencing factors

of foam blocking ability in theprocess of foam flooding are

numerous, and play a role simultaneously, hence it is veryvaluable to quantitatively characterize the foam resistance

factor under multiple scenarios. Also, it is beneficial to the

advancement of numerical simulation technology of foam

flooding. Therefore, a novel foam resistance factor model

that comprehensively considers the influences of the above

factors is achieved:

Rkfcs; g; k; T; So

ArRfjkkc

1 1kD1mkD

n

h i 1 exp 3g

b

expc So

1 a expr cs 1 exp Ta

b h i19

ArRfjcsCMC Rf

ggc

Rf

TTrRf

So0

RfjTest4

20

The validation of the multi-factor gas mobility model

can be verified by the experimental data, which is shown

inFigure 6. The values of the undetermined coefficients

are shown inTable 1.



7/17

Equation (19) not only comprehensively considers the

influences of the rock properties, fluid properties and

surroundings on foam block characteristics, but also

avoids the discontinuous behavior of gas mobility

caused by the critical foaming agent concentration and

critical oil saturation, which will greatly improve the sta-

bility of the numerical simulation process.

Correction of the Resistance Factor for Weak Foam

It was reported that flow resistance is small and foam

textures are coarse, consistent with the injection of un-

foamed gas or weak foam in the inlet region, and there

exists a strong foam piston-like front moving through

the porous media [6, 44]. This phenomenon has also

been verified by many experiments [45, 46]. However,

most of the existing foam flow models cannot simulate

this process [6]. In this model, the above resistance fac-

tor model is based on strong foam, so the following

correction function is introduced to represent thiseffect:

RfL R0kf

1 AA expRR L 21

whereRkf0 is the resistance factor of strong foam;L is the

flow distance of weak foam or unfoamed gas and

foaming agent solution, m; AA and RR are model

coefficients.

1.3.2 Adsorption Model for the Surfactant

The adsorption of the foaming agent will occur when

it flows in the porous media and obeys the typical

Langmuir law:

cs csmaxbscs

1 bscs22

where bs is the Langmuir parameter, (kg/m3)1; csmax is

the maximum adsorbed concentration, kg/kg.

1.3.3 Capillary Desaturation and InterfacialTension Model

The foaming agent can also reduce the oil-water interfa-

cial tension by its surfactant characteristics and decrease

the residual oil saturation [47]:

Sor Sormin Sor max Sor min

1 ANNco23

Ncolwvw

rwo24

rwo ar 10brcs 25

where Nco is the capillary number; row is the oil-water

interfacial tension, mN/m; Sor minis the limit of residual

oil saturation under a high capillary number; Sor max is

the residual oil saturation under a low capillary number;

ar

, br

and ANare undetermined coefficients.

500

400

300

200

100

00 100 200 300

y= x

400 500

Experimental valuea) b)

500

400

300

200

100

00 100 200 300

y= x

400 500

Experimental value

Calcu

lationvalue

Calcu

lationvalue

Figure 6

Validation of the multi-factor gas mobility model using experimental data. a) Surfactant #1, b) Surfactant #2.


7


8/17

1.3.4 Relative Permeability Model

The Stone II model is used to calculate the three-phase

relative permeability [48]:

krw krwroSw Swc

1 Swc Sorw

nw26

krow krocw1 Sw Sorw1 Swc Sorw

now27

krog krocw1 Swc Sorg Sg

1 Swc Sorg

nog28

krg krgroSg Sgc

1 Swc Sorg Sgc

ng29

kro f3 Sw; Sg krocwkrow

krocw krw

krog

krocw krg

krw krg

30

where krocwis the oil phase relative permeability corre-

sponding to connate water; krw and krg are the water

and gas phase relative permeability, respectively; krowand krog are the oil phase relative permeability in the

oil-water system and oil-gas system, respectively; nw,

now, nw, nog andng are input parameters; Swc, Sorw, SgcandSorgare the end-points in oil-water and oil-gas sys-

tems relative permeability functions.

1.3.5 Physical Properties of the Gas Phase [49]

The formation volume factor is:

Bg 3:458 104 Z

273 t

pg31

The expansion factor is:

Eg 1

Bg 2891:7

pg

Z273 t 32

where Zis the compressibility factor; t is the reservoir

temperature, C.

1.3.6 Capillary Pressure Model

Capillary pressure is a function of saturation:

pcowSw A1 ffiffiffiffi

/k

r S

w Swc1 Swc Sor

B1

33

pcgoSg A2

ffiffiffiffi/

k

r

Sg Sgc1 Sgc Sor

B234

where A1 and A2 are input parameters; B1 and B2 are

capillary pressure exponents.

2 SOLUTION AND VALIDATION OF THE MATHEMATICALMODEL

2.1 Solution Method

In this model, gas flow velocity is used as the triggering

mechanism; water saturation obtained based on DLVO

theory is used for the bubble collapse mechanism. If

foam exists in the porous media, the foaming agent con-

centration, foam quality, permeability, temperature and

oil saturation come into play for calculating the resis-

tance factor in the grid. This method avoids solving

the foam population balance equation. A method for

solving this mathematical model is as follows:

the IMPES (Implicite Pressure Explicite Saturation)method is used to solve the pressure and saturation

equations to obtain the pressure and saturation distri-

butions for each phase;

the classical four-order Runge-Kutta method is

applied to solve the concentration equation of the

foaming agent;

the local gas flow velocity, critical gas flow velocity

and critical water saturation based on the grid pres-

sure and saturation are solved;

TABLE 1

Values of undetermined coefficients

Surfactant #1

a r b m n a b c Rf|Test Rf|c=CMC Rf|g=g0 Rf|T=Tr Rf|So=0 Rf|k=kc

100 19.5 60 3 2 140 30 9.0 139 139 156 150 139 430

Surfactant #2

a r b m n a b c Rf|Test Rf|c=CMC Rf|g=g0 Rf|T=Tr Rf|So=0 Rf|k=kc

230 16 45 8.5 1.05 70 38 9.2 279 300 285 360 279 390



9/17

the critical generation condition and critical collapse

condition are used to determine whether there is foam

in the grid. If foam exists in the grid, using permeabil-

ity, the foaming agent concentration, gas-liquid ratio,

temperature and oil saturation are used to calculate

the resistance factor; otherwise, the resistance factor

is set to one;

then the resistance factor will be substituted into the

gas flow equation;

repeat steps (1-5) until the end of the simulation time.

2.2 Validation of the Novel Model

In the Absence of Oil

The model includes all mechanisms that are:

crucial to the process;

known with reasonable accuracy.

With the purpose of validating the model, the foam

flow data obtained from Kovscek [44] is used. Core

and fluid data are based on reference [44], and other

model parameters are listed inTable 2. The fitting result

of the multi-factor model shown inFigure 7is a slightlybetter fit than the population balance model although

the curve for 0.23 PV is not a close fit due to the lack

of strong foam and gas channeling.

In the Presence of Oil

Because the impact of oil presence is considered, one

group of foam flooding experimental data is also used.

In this experiment, foaming agent solution (SDS: surfac-

tant #1) with the concentration of 0.4 wt% was injected

continuously into linear unconsolidated media of length

0.3 m at a rate of 2 mL/min, while gas was also injectedcontinuously to give a foam quality of 80% at the

sandpack entrance. The permeability is 4.5 lm2 and

porosity is 0.33. The initial oil saturation is 0.4 and oil

viscosity is about 2.0 mPas. At 120 min, continued water

flooding was performed at a rate of 5mL/min. Other

model parameters are listed inTable 3. The comparison

between computed and experimental data is shown in

Figure 8and the agreement is excellent.

3 RESULTS AND DISCUSSION

In order to study thoroughly the differences between thefoam flooding with the gas-water flooding and the

influences of many parameters on the EOR effect, a syn-

thetic geological model is built. The reservoir scale is

10 9 10 9 2 with the dimensions of dx = dy = 10 m

and dz = 5 m, as shown in Figure 9. The time step is

1 d. The reservoir temperature is 30C and pressure is

20 MPa. The viscosity of oil is 20 mPas and initial oil

saturation is 0.8. The porosity is 0.3, and the permeabil-

ity is 1 lm2 and 4 lm2 for the top and bottom layers,

respectively. The ratio of vertical permeability to hori-

zontal permeability is 0.1. The production rate is

20 m3/day, with an injection-production ratio of 1:1The foam is injected when the water-cut reaches 90%

(t = 2 000 d) and the slug size is 0.4 PV. The foaming

agent concentration is 0.5 wt% and the injection gas-

water ratio is 1:1 in formation conditions. The gas vis-

cosity is 0.03 mPas and the water viscosity is 1.0 mPasThe difference between gas-water flooding and foam

flooding is that the foaming agent concentration equals

zero or not. Other model parameters are listed

inTable 4.

TABLE 2

Parameter values for simulations of Kovsceks experiment

a r b m n a b Ar

100 19.5 60 8 1.1 140 30 2.0

Rf|k=kc aJ bJ a1 b1 AA RR

1 200 1.3 0.9 0.1 1.5 80 40

2

000

1

600

1

200

800

400

00

0.23 PV

0.46 PV

0.68 PV

3.0 PV

0.2 0.4 0.6 0.8 1.0

Dimessionless distance, x(L)

Experimental value

Population balance model

Multi-factor model

Pressure

drop

(kPa)

Figure 7

Comparison between the computed value using the multi-

factor model, Kovsceks coreflood data, and the computed

value using a population balance model


9


10/17


11/17

2500

days

Water + gasflooding

a) L1

c) L1

b) L2

d) L2

e) L1 f) L2

g) L1 h) L2

Foam

flooding

2750days

Water + gasflooding

Foam

flooding

0.28

0.50 0.30

0.27

0.24

0.21

0.18

0.15

0.12

0.09

0.06

0.03

0

0.28 0.10

0.08

0.06

0.04

0.02

0

0.24

0.20

0.16

0.12

0.08

0.04

0.45

0.40

0.35

0.30

0.25

0.20

0.150.10

0.05

0

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.100.05

0

0.50

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.100.05

0

0.20

0.16

0.12

0.08

0.04

0

0.24

0.20

0.16

0.12

0.08

0.04

0

Figure 10

Distribution of gas saturation at different times by foam flooding and water + gas flooding.


11


12/17

higher oil saturation in L1, the resistance factor is lower,

which results in the gas phase area being larger in L1. When

t= 2 750 d, the gas has already channeled to the producer

alongtheL1, and the gas saturationis close tozero intheL2for water + gas flooding. Conversely, gas channeling does

not appear and the gas saturation is still about 0.3 and

exists in the form of foam in L2 for foam flooding. The

foam located in L2 makes water divert into the lower-permeability strata (L1) and displaces more additional

remaining oil than water + gas flooding.

The development effects of different methods are shown

inFigure 11. It is clear that the ultimate recovery order is

foam flooding (48.8%) > water + gas flooding (46.7%)

> water flooding (43.7%) and the flood-response time of

water + gas flooding is earlier and shorter than foam

flooding because of the densities of water, oil and gas.

Due to gravitational differentiation, both top and bottom

layers are well swept by gas and water, so the ultimate

recoveryof water+ gas floodingis larger than waterflood-

ing. In the foam flooding process, some of the unfoamed

gas flows in the top layer to sweep the remaining oil, and

some of the gas in the form of foam flows in the bottomlayer. As previously analyzed, the blocking ability of foam

in the high-permeability layer is stronger than in the low-

permeability layer. As a result, the gas flows in the high-

permeability layer the same as in the low-permeability

layer, and more water enters the lower-permeability layer

and consequently displaces more oil. Hence, foam can

both effectively inhibit the gas override and establish a

large flow resistance to realize the fluid diversion, which

is favorable for enhancing oil recovery in heterogeneous

reservoirs.

3.2 Sensitivity Analysis of Foam Flooding EnhancingOil Recovery

In a lab study, foam flooding can enhance oil recovery by

more than 20% in suitable conditions. Actually, most of

the fields in China have carried out foam flooding and

obtained satisfactory results [4], but the incremental oil

recoveries are less than lab results due to their adverse

conditions. Hence, studying the effects of reservoir and

foam properties for choosing suitable reservoirs to per-

form foam flooding is very important. The permeability

max-min ratio, ratio of vertical to horizontal permeabil-ity, depositional sequence, reservoir temperature, foam

20

16

12

8

4

0 0

10

20

Oilrecovery(%)

Oilproductionrate(m3/d

)

30Water flooding

Foam flooding

Water + gas flooding

40

50

0 1000 2000 3000 4000

Time (d)

5000 6000 7000 8000

Figure 11

Development effects of different methods.

TABLE 5

Parameters of simulated projects for sensitivity analysis

Influence factors Kr kv/kh g(%) Sequence Concentration

(wt%)

Temperature

(C)

Kr 2, 4, 6, 8, 10, 12,

15

0.1 50 Transgressive 0.5 30

kv/kh 4 0.01, 0.05, 0.1,

0.5, 1.0

50 Transgressive 0.5 30

g 4 0.1 20, 25, 33, 40, 50,

66, 75, 80, 90

Transgressive 0.5 30

Depositional

sequence

4 0.1 50 Transgressive,

regressive

0.5 30

Foaming agent

concentration

4 0.1 50 Transgressive 0.1, 0.2, 0.3, 0.4,

0.5, 0.6, 1.0

30

Reservoir

temperature

4 0.1 50 Transgressive 0.5 30, 60, 90, 120,

150, 180



13/17

quality and foaming agent concentration are very practi-

cal, common and important influencing factors in actual

oilfields. Therefore, we performed a sensitivity analysis

of these factors using the above heterogeneous reservoir

and parameters. The parameters of the simulated pro-

jects are shown inTable 5.

3.2.1 Permeability Max-Min Ratio

The permeability max-min ratio is defined as the ratio ofthe highest permeability to the lowest permeability.

Because foam has the feature of big block and not small

block, if the reservoir has a suitable permeability max-

min ratio, the EOR effect will be superior. Figure 12 shows

the ultimate and incremental oil recoveries for different

permeability max-min ratios. It is shown thatwhen theper-

meability max-min ratio is small, the incremental oil recov-

ery increases sharply as the ratio increases; when it reaches

10, the oil recovery increment reaches a plateau. The rea-

sonfor this is the lower the permeability max-min ratio will

result in the closer the permeability of each stratum. From

Equation (10), the foam resistance factor is a function ofpermeability. For a smaller permeability max-min ratio

reservoir, after foam flooding, the water diverting into

the low-permeability layers is lowered; for a larger perme-

ability max-min ratio reservoir, the foam resistance factor

is larger in the high-permeability layer and more water

diverts into the low-permeability layer to sweep the

remaining oil. Due to the limited blocking capacity of

foam, the foam strength decreases if the permeability is

too large. Therefore, the ultimaterecovery is not verygood

for a reservoir with an extremely large permeability max-

min ratio. Consequently, foam flooding is suitable for res-

ervoirs with a moderate permeability max-min ratio.

3.2.2 Ratio of Vertical to Horizontal Permeability

Override is a problem in gas flooding. In gas flooding,

the ratio of vertical to horizontal permeability should

be considered.Figure 13shows the ultimate and incre-

mental oil recoveries for different ratios of vertical tohorizontal permeability. It is shown that as the ratio

of vertical to horizontal permeability increases, the

incremental oil recovery sharply decreases. When the

ratio is bigger than 0.2, the incremental oil recovery

decreases slowly and is only about 2%. The reason is

that if the ratio of vertical to horizontal permeability

is large, the gas gravitational variations will be more

pronounced. As a result, all the injected gas overrides

into the top layer, and no foam is generated in the bot-

tom layer. The continued water diversion would not

take place. Therefore, foam flooding is suitable for res-

ervoirs with a lower ratio of vertical to horizontal per-meability.

The depositional sequence is defined as the regula-

tion by which the sand particles deposit in sequence

to form rock strata. A transgressive depositiona

sequence is composed of several sand layers where

the sand diameter declines from the bottom to the

top, i.e. the permeability is reduced in the vertical pro-

file from the bottom to the top; a regressive deposi-

tional sequence is just the reverse. The depositiona

20

30

40

50

60 9

8

7

6

5

4

Ultimaterecovery(%)

Oilrecovery

increment(%)

Foam flooding

Increment

Water flooding

0 3 6 9 12 15 18

Permeability max-min ratio

Figure 12

Ultimate recovery and increment vs permeability max-min

ratio.

Foam flooding

55

52

49

46

43

400 0.2 0.4 0.6 0.8 1

1

2

4

6

8

10

Water flooding

Increment

Ratio of vertical to horizontal permeability

Ultimaterecovery(%)

Oilrecove

ryincrement(%)

Figure 13

Ultimate recovery and the increment vs ratio of vertical to

horizontal permeability.


13


14/17

sequence has a significant influence on the gas override

to affect the ultimate recovery. Figure 14 shows the

development effects with different displacing modes

and depositional sequences. Apparently, the oil recov-

ery in a regressive depositional sequence reservoir is

higher than that in a transgressive depositional

sequence reservoir for all the three displacing modes.

The water + gas flooding oil recovery is higher than

water flooding. However, the incremental oil recovery

in regressive depositional sequence reservoirs is lowerthan transgressive depositional sequence reservoirs.

The foam flooding oil recovery is higher than water

+ gas flooding. However, the incremental oil recovery

in a regressive depositional sequence reservoir is higher

than in a transgressive depositional sequence reservoir.

For the rationale, in transgressive depositional

sequence reservoirs, water is inclined to enter the

high-permeability layer due to gravitational variations

and lower flow resistance, which results in some

remaining oil being confined within the low-

permeability layer; continued gas is inclined to override

into the low-permeability layer under the gravitationalvariations and displaces the remaining oil. In the

regressive depositional sequence reservoirs, due to

gravitational variations and lower flow resistance, both

the high-permeability and low-permeability layers are

well swept by water, and the remaining oil is lowered

in the high-permeability layer (top layer); the gas is still

inclined to enter the top layer due to gravitational vari-

ations and lower flow resistance, but the EOR effect is

not obvious. Comparing foam flooding with water +

gas flooding, in the transgressive depositional sequence

reservoirs, more gas flows in the low-permeability lay-

ers, and the amount of foam in high-permeability lay-

ers is less than regressive depositional sequence

reservoirs, which results in less water diverting into

lower-permeabilitylayers after foam flooding. Conversely,

in the regressive depositional sequence reservoirs, since

more gas flows in the high-permeability layers,

consequently, this results in more flow of foam in high-

permeability layers as well. As a result, more water divertsinto lower-permeability layers after foam flooding.

3.2.4 Reservoir Temperature

Figure 15 shows the variation of ultimate oil recovery

with reservoir temperature. The ultimate oil recovery

decreases as the temperature increases. When the tem-

perature is lower than 100C, the ultimate oil recovery

varies very little; when the temperature is between 100

and 200C, the ultimate oil recovery decreases sharply;

when the temperature exceeds 200C, the ultimate oil

recovery of foam flooding is close to that of water +gas flooding. Therefore, the reservoir temperature

should not be high, or temperature-tolerant foaming

agents should be used for high-temperature reservoirs.

3.2.5 Foam Quality

Foam quality is an important factor determining the

blocking capacity of the foam texture.Figure 16shows

the ultimate oil recovery of different foam qualities.

60

50

40

30

20

10

00 2000 4000

Time (d)

6000

Water flooding-trangressive

Gas-water flooding-transgressive

Foam flooding-transgressive

Water flooding-regressive

Gas-water flooding-regressive

Foam flooding-regressive

8000

Oilre

covery(%)

Figure 14

Comparison of the developments effects with different

methods and depositional sequences.

49.0

48.5

48.0

47.5

47.0

46.5

46.0

Ultimate

recovery(%)

Water + gas flooding

0 50 100 150 200 250 300

Temperature (C)

Figure 15

Ultimate recoveryvs reservoir temperature.



15/17

Evidently, as the foam quality increases, the ultimate oil

recovery first increases and then decreases with an optimal

value of 50%. This is due to the fact that a lower foam

quality means a thicker lamella and a smaller bubble;

under these conditions, the Jamin effect [51] is very small;conversely, a higher foam quality leads to a thinner

lamella, a faster gas velocity and a bigger bubble; under

these conditions, the bubble is more likely to collapse by

shearing when it flows through the porous media. There-

fore, a more stable bubble with a better Jamin effect can

obtain a better EOR effect. Based on the relation between

the foam quality and gas-water ratio, the optimal injec-

tion gas-water ratio should be chosen at the volume ratio

of 1:1 under the reservoir conditions.

3.2.6 Foaming Agent Concentration

Figure 17 shows the variation of ultimate oil recovery

with foaming agent concentration. Noticeably, the ulti-

mate oil recovery reaches a plateau at 0.6 wt% after

increasing along with the foaming agent concentration

Based on the parameters used in this case, the CMC is

about 0.5 wt%. Optimal concentration is a little higher

than the CMC since some of the foaming agent is

adsorbed on the rock. So, the foaming agent concentra-

tion of foam flooding should be a little higher than the

CMC of the surfactant.

CONCLUSIONS

A novel model of multi-factor foamflooding is established

The IMPES method in conjunction with a fourth-order

Runge-Kutta method were used to solve the governing

equation. The validation of this model was confirmed by

matching the experimental data. Finally, the effects of several parameters including the permeability max-min ratio

ratio of vertical to horizontal permeability, depositional

sequence, foam quality, foaming agent concentration

and reservoir temperature on oil recovery were studied.

The following are the main conclusions:

1) A foam resistance factor model considering the

influences of permeability, foaming agent concen-

tration, foam quality, temperature and oil satura-

tion is obtained. Then, taking the gas velocity as

the foam generation condition and water satura-

tion as the foam collapse condition, the gas mobil-

ity model was achieved;2) Foam can effectively weaken the phenomena of gas

override in the vertical direction due to gravita-

tional variations and gas channeling in a horizontal

direction caused by large gas mobility;

3) The mechanism of water + gasflooding enhancedoil

recovery is that due to the gravitational variations,

gas increases the swept area of the injected fluid;

and the mechanisms of foam flooding are both the

gravitational variations and the water diversion;

4) With a smaller permeability max-min ratio, the

incremental oil recovery increases sharply and

reaches a plateau at the ratio of 10. Foam floodingis suitable for reservoirs with a moderate perme-

ability max-min ratio (kr= 5-10);

5) As the ratio of vertical to horizontal permeability

increases, the incremental oil recovery sharply

decreases. When the ratio is bigger than 0.2, the

incremental oil recovery decreases slowly, and is

only about 2%. Foam flooding is appropriate for

reservoirs whose ratio of vertical to horizontal per-

meability is lower than 0.2;

50

49

48

47

46

45

Ultimaterecovery(%)

0 0.2 0.4 0.6 0.8 1.0Foaming agent concentration (wt%)

Figure 17

Ultimate recoveryvs foaming agent concentration.

50

49

48

47

46

45

Ultimaterecovery(%)

0 20 40 60 80 100

Foaming quality (%)

Figure 16

Ultimate recoveryvs foam quality.


15


16/17

6) The oil recovery in regressive depositional sequence

reservoirs is higher than that of transgressive depo-

sitional sequence reservoirs for water flooding, gas-

water flooding and foam flooding. The gas-water

flooding incremental oil recovery for water flooding

in regressive depositional sequence reservoirs is less

than that in transgressive depositional sequence res-

ervoirs, but the foam flooding increment for water+ gas flooding in regressive depositional sequence

reservoirs is more than that in transgressive deposi-

tional sequence reservoirs;

7) The ultimate recovery decreases as the temperature

increases. The reservoir temperature should not be

high for foam flooding; otherwise, temperature-tol-

erant foaming agents should be used for high-tem-

perature reservoirs;

8) As the foam quality increases, the ultimate oil

recovery first increases and then decreases, and

the optimal value is 50%. The optimal injection

for the gas-water ratio should be chosen at the vol-ume ratio of 1:1 under the reservoir conditions;

9) Due to adsorption of the surfactant, the foaming

agent concentration during foam flooding should

be a little higher than the CMC of the surfactant.

ACKNOWLEDGMENTS

This study was funded by the Chinese National Natural

Science Foundation (51274212) and Important National

Science & Technology Specific Projects of China

(2011ZX05014-003-008HZ).

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Manuscript accepted in April 2014

Published online in July 2014

Copyright 2014 IFP Energies nouvelles

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A Novel Model of Foam Flooding Considering Multi-Factors for Enhancing Oil Recovery

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